Aircraft: SMALL TRANSPORT; LOW WING; 2 TURBOPROP ENG
Phase of flight: Landing
Anomaly: Conflict Ground Conflict; Critical; Deviation / Discrepancy - Procedural FAR; Deviation / Discrepancy - Procedural Published Material / Policy

While landing at PTS on runway 34 during the roll out; another airplane; while either taking off or landing on runway 22 was observed to our right on the runway approximately 700 ft from us travelling in a Southwest direction. The airplane pitched up and banked to his left to go behind us. There was no radio broadcast heard from the other airplane or lights observed on the airplane. I was the Second-in-command (Pilot Not Flying) and not required by FAR. The following used information extracted from the G1000 data logging files for time; distance and frequency change information. We were on an IFR flight plan direct route to PTS.We had been monitoring the PTS AWOS and the XM weather for Pittsburg as being clear with calm winds; altimeter setting was 30.08.We began a VNAV computed descent to PTS runway 34. When descending through 10;000 ft; the 'Descending 10;000 ft' checklist was completed which included turning on the Pulse Recognition Lights. The Nav; Beacons and Strobe lights were already on.14 miles South of Pittsburg; I switched COM2 to the PTS CTAF and keyed up the runway lighting. The REIL and VASI for runway 34 became immediately visible. It's my recollection I made a position report at that time to Pittsburg Airport and traffic on Com2. I continued to monitor the PTS CTAF and Kansas City Center frequencies as we proceeded toward the airport. PF (Pilot Flying) monitored Kansas City Center.10 miles south of the airport; Kansas City Center gave us an airport position report at which time I reported the airport in sight for the visual approach and cancelled IFR in concurrence with the PF. Kansas City Center acknowledged the cancellation and advised that he had no radar observed traffic between us and the airport. At 9.6 miles; I changed Com1 to the PTS CTAF and broadcast a position report to 'Pittsburg airport and traffic' and noted one 'White Diamond' TCAS target on the MFD several miles North of the airport that was well North of the Airport when we landed. At 7 miles out; I activated the final approach leg as the active leg. The PF intercepted and flew the final approach course. When near the final approach fix; the Landing Gear was extended; and the Taxi and Landing lights were turned on. It's my recollection I continued to broadcast position reports at about 5; 3 and 1 mile as we continued final approach to runway 34 via the RNAV 34 LPV approach procedure. There were no radio broadcasts on the PTS CTAF from any source while monitoring. Inside of one mile; I scanned the airport for other traffic and particularly along runway 34 for wildlife. I announced to the PF that I did not see deer or anything and he concurred. The 'White Diamond' target previously noted was still north of the airport. There were no other TCAS targets observed in the vicinity.As we continued over the threshold and the PF began his flare to landing nearing the fixed distance markers; we received a generic visual yellow 'TAFFIC ALERT' box on our Primary Flight Displays. I do not recall hearing an aural alert. A 'Traffic Alert' is not uncommon on or near an airport and often occurs when a pilot turns his transponder on while operating on the surface of the airport or preparing to take-off. We scanned for traffic and after touchdown; just prior to the intersection of runway 34/22; I observed Aircraft Y which appeared to be accelerating for take-off from runway 22. Both PF and PNF (Pilot Not Flying) observed the aircraft pitch up and bank to the left over the runway 22 VASI lights as we cleared the intersection. There was no radio transmission heard from Aircraft Y at any time nor was any lights observed on the aircraft. We were much closer to the intersection and much faster than Aircraft Y so it was obvious the best course of action for us was to clear the intersection without delay or braking. It is my opinion that if the other pilot saw us when I first saw him; he could have stopped before getting to the intersection.Once we had cleared the intersection on rollout; I made several blind calls to the 'Aircraft Y at Pittsburg' with no answer. After a brief period; while back taxiing on runway 34 to the terminal; the pilot in Aircraft Y made a call and advised he had just landed at Pittsburg and did not hear our calls until he switched to his other radio. Aircraft Y was parked on the terminal ramp when we got to the ramp. A brief conversation with the pilot indicated that he thought one of his radio may have failed and didn't hear us until he switched radios. I also advised him that we did not see any lights on his plane. As we were starting up for departure; we observed him checking his lights which they appeared to work. Though Aircraft Y's pilot comment that he had just landed; it was my impression he may have landed on the remaining runway after we passed through the intersection after he made a takeoff attempt. The fact there was no traffic target on TCAS when we were approaching the airport and a 'TRAFFIC ALERT' while we were landing would be consistent with his transponder being turned on as he took the runway for take-off. He also appeared to be accelerating when I first saw the airplane. The natural lighting condition at the time was transitional from sunset to dusk where objects; particularly unlit; contrasted with background may be difficult to see. The run-up pad for runway 22 sets to the South of the end of the runway with a large group of trees about 50 ft from the edge of the pad. For the time of year; there still appeared to be significant foliage on the trees. Also; an airplane; particularly a mostly white airplane; sitting on the white painted area at the end of the runway would be difficult to see. A post flight inspection of the lights on our aircraft was completed to confirm proper operation. The Landing; Taxi; Navigation; Strobe and wing-tip Pulse Recognition lights were all operating properly. The frontal lighting consists of 2 bright LED landing lights; 1 bright LED taxi light; 2 bright LED navigation lights on each wing tip; 1 white top of tail flashing beacon light; 1 white belly flashing beacon light; 1 bright white flashing strobe on each wing tip and tail and 1 white pulsing recognition light on each wing tip.All proper communication frequency selections and distances were confirmed by reviewing the Data Logs of the G1000 avionics system installed in our aircraft. Calm winds at an uncontrolled airport with multiple runways was a contributing factor. GA pilot reported a ground conflict at an intersecting runway during rollout.